2025 HSC Mathematics Extension 1
Question 6:
Inverse trigonometric functions
Given that is a non-zero constant, which of the following integrals is equal to zero?
How to recognise this question
Question type: inverse trigonometric functions
- The command and notation point to inverse trigonometric functions.
- The requested response is a multiple choice.
How to handle it: use the restricted domain and range that make the inverse function single-valued.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- is odd and is even.
- Therefore is odd.
- An odd integrand has integral zero over , so option D is correct.
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 1 total mark for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
Sketch , stating its domain, range and three key points.
Question 2
Evaluate .
Question 3
Differentiate and find .